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President Barack Obama committed Tuesday to working with Gov. Gary Herbert to see if the state could beef up a requirement that poor Utahns seek work before getting health coverage under the governor's proposed Healthy Utah plan.

The work requirement was a major sticking point in negotiations with the Department of Health and Human Services. Herbert has argued that those who get coverage should also look for a job and a way off public-health insurance, but the administration dug in its heels, saying coverage should not be contingent on the job search.

Ultimately, Herbert agreed to a watered-down requirement. But in a nearly hourlong meeting in the White House's Oval Office between the president and governors on Tuesday, Obama committed to seeing if the administration might be able to give some ground on the issue.

''He was very positive about that concept and as we had discussion back and forth, his response was, 'Let me call Secretary Sylvia Burwell and see if we can't revisit this discussion and get closer to where you want to be,' '' Herbert said.

"If the door is not closed absolutely to what I've been trying to accomplish with the work requirement, I'm anxious to see what happens here in the next few days, frankly," the governor said during a conference call.

Herbert has pitched his Healthy Utah plan as an alternative to the straightforward expansion of Medicaid called for under the Affordable Care Act, commonly referred to as Obamacare.

Under Herbert's proposal, the federal government would pay the costs for the first three years to cover 95,000 of the poorest uninsured Utahns who don't currently qualify for Medicaid.

Over time, the federal portion of the program will be phased down to 90 percent, meaning the state will have to pick up 10 percent of the cost. Legislative leaders are concerned that the governor's program commits the state to the program long-term and will eventually cost Utah $93 million a year. A legislative health-reform task force recommended against adopting Herbert's plan.

Incoming House Majority Leader Jim Dunnigan, R-Taylorsville, said it remains to be seen how much additional flexibility on the work requirement will matter to members of the Legislature, and it likely depends on how much the White House is willing to give.

"I applaud the governor for continuing the dialogue," Dunnigan said.

Dunnigan, who chairs the Health Reform Task Force, said the concern they had was with major changes to the estimated cost in pulling the plug on coverage for those above the poverty line if the state decides to discontinue the program after the three-year pilot project.

Cost estimates ballooned from about $40 million to $136 million to discontinue the program.

"What that means is the fallback plan has been taken away," Dunnigan said. "Our parachute was shredded."

During his trip to Washington, Herbert also met with Gen. Mark Welsh III, chief of staff of the U.S. Air Force, to discuss the future of Hill Air Force Base and the proposed 700,000-acre expansion of the Utah Test and Training Range in Utah's west desert.

"We talked about how important it was to make sure the local governments, those people impacted by any expansion of the test and training range, ought to be brought into the circle and discuss the impacts before any decision to go ahead," Herbert said.

Herbert was in Washington for the semi-annual meeting of the National Governors Association, where governors from around the country gather to discuss policy issues and the state's interaction with the federal government.

Herbert and Colorado's Democratic Gov. John Hickenlooper, delivering the NGA's State of the States Address, called on Congress and the Obama Administration to partner with governors and states on an array of issues — from education to transportation to environmental protection — to deliver the kind of results Americans want.

"Like many of my fellow governors, I have been frustrated by the stalemate that seems to pervade Washington," Herbert said. "With a backlog of work that has been left undone by the previous Congress, we now have the opportunity for meaningful reform to ensure that state-federal programs work more effectively."